i have a problem with that, ca you help me ?

Question

Five bottles of water and 3 bagels cost $13.53. At the same prices, 4 bottles of water and 6 bagels cost $13.92. Find the price per bottle of water and the price per bagel.

Answer 1

Hi Deborah, set up a system of equation with the given information.

 

Let w represent the water and b represent the bagels.

 

Equation 1, 5 bottles of water and 3 bagels:

 

5w + 3b = 13.53

 

Equation 2, 4 bottles of water and 6 bagels:

 

4w + 6b = 13.92

 

System to solve:

 

5w + 3b = 13.53

4w + 6b = 13.92

 

Multiply equation 1 by -2 and add:

 

-10w  - 6b = - 27.06

   4w + 6b =   13.92

------------------------

-6w = -13.14

 

w = 2.19

 

Substitute for w in equation 2 to find b:

 

4 * 2.19 + 6b = 13.92

 

8.76 + 6b = 13.92

 

6b = 5.16

 

b = .86

 

Therefore, the water costs $2.17 per bottle and the bagels cost $.86 each.

 

Check using equation 1:

 

5 * 2.17 + 3 * .86 = 13.53

 

10.85 + 2.58 = 13.53

 

13.53 = 13.53

 

Values check.

 

Questions?